Ehrhart Limits

TL;DR

This paper introduces Ehrhart limits as formal power series arising from sequences of Ehrhart h*-polynomials, exploring examples mainly involving reflexive polytopes and simplices.

Contribution

It defines Ehrhart limits and identifies various sequences of polytopes, especially reflexive polytopes and simplices, that produce these limits.

Findings

Ehrhart limits are formal power series as limits of Ehrhart h*-polynomials.

Sequences of reflexive polytopes and simplices can generate Ehrhart limits.

The paper provides examples illustrating the concept of Ehrhart limits.

Abstract

We introduce the definition of an Ehrhart limit, that is, a formal power series with integer coefficients that is the limit in the ring of formal power series of a sequence of Ehrhart $h^*$-polynomials. We identify a variety of examples of sequences of polytopes that yield Ehrhart limits, with a focus on reflexive polytopes and simplices.